Integrated Production, Inventory, and Location-Allocation Decisions in Designing Supply Chain Networks

Integrated Production, Inventory, and Location-Allocation Decisions in Designing Supply Chain Networks

Sepideh Alavi (University of Wisconsin-Milwaukee, Milwaukee, WI, USA), Nader Azad (Sobey School of Business, Saint Mary's University, Halifax, Canada), Mojtaba Heydar (University of Newcastle, Callaghan, Australia) and Hamid Davoudpour (Amirkabir University of Technology, Tehran, Iran)
DOI: 10.4018/IJISSCM.2016100102


This paper studies the design and development of an inventory model for manufacturers with constant production rates considering location and allocation decisions in a three-level supply chain. In this supply chain, the demands of customers and the lead times are assumed to be uncertain. Therefore, each distribution center retains some amount of safety stock to provide suitable service level for customers. The proposed non-linear model aims to minimize location and inventory costs of distribution centers, manufacturers and transportation costs subject to relevant constraints. To solve the model, an efficient imperialist competitive algorithm and a Tabu search algorithm, each using variable neighborhood search, are proposed. The model outputs are decisions such as which distribution centers and manufacturers are opened, the allocation of customers to distribution centers, and distribution centers to manufacturers. Results are also the ordering quantity of each opened distribution center and the production rate of each opened manufacturer. The computational results for several instances of the problem are represented to show the efficiency of proposed algorithm.
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In today’s competitive and dynamic market conditions, the effective collaboration of partners and coordination of all strategic, tactical, and operational activities and decisions within the supply chain is prerequisite (Shen, 2005). Recently, lots of integrated models have been studied within the supply chain networks approach. The integrated models in supply chain networks include inventory-routing problems, location-inventory problems, and production-inventory models (Tarantilis, 2008). This paper mostly deals with location-inventory problems integrated with production rates’ decision for manufacturers.

The previous related works on integrated models can be viewed and classified based on the level of integration, complexities, decision variables, modeling techniques, and solution algorithm. In what follows, these related works are briefly discussed.

The first classification is the level of integration which include location-inventory, inventory-routing, and production-inventory. There are many researchers who developed models for location-inventory problems. Erlebacher and Meller (2000) develop a non-linear model for distribution centers’ locations accompanied with inventory holding costs at DCs (Distribution centers) in which the location of DCs were assumed discrete variables. Teo, Ou, and Goh (2001) propose a location-inventory model which considered centralization of DCs and did not include transportation costs. The models in this category are further developed by other researchers to include more decision variables and factors. In one study, Daskin, Coullard, and Shen (2001) develop an integrated approach to determine the location, number of the DCs and the amount of safety stock hold at each DC. They develop a nonlinear integer program solved by a Lagrangian Relaxation solution algorithm. The outputs of their approach are number of DCs to be established along with the level of inventory to be kept at each DC. In another study, Miranda and Garido (2004) work on a nonlinear three-level location-inventory model with capacitated DCs. The manufacturers are pre-determined with no inventory hold at them. They developed a mixed integer nonlinear programing, and a Lagrangian-based heuristic and sub-gradient method were developed in order to solve that. Miranda and Garido (2006) develop a hierarchical two-phase heuristic in order to optimize the service level in a three level distribution network design. In the first phase, the service level is optimized and in the second level, location-inventory decision is considered. These two steps are iterated until equilibrium is reached with regard to service level. Berman, Krass, and Tajbakhsh (2012) consider a location-inventory model where DCs follow a periodic review inventory policy. The aim is to determine inventory policy parameters at the DCs together with location- allocation decisions. A Lagrangian relaxation algorithm is proposed to solve the model. In a problem that can be considered as location-inventory, Askin, Baffo, and Xia (2014) develop a model for logistics network and warehouse location with inventory consideration. The model solved by a genetic algorithm which is problem specific.

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